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A371457 Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a progression of the form p, p-q, p+q, where q >= 0.

%I A371457 #41 Jun 02 2024 21:33:18
%S A371457 1,1,2,1,1,2,2,3,3,1,1,2,1,1,2,2,4,3,2,6,5,5,6,3,4,3,4,1,1,2,1,1,2,2,
%T A371457 3,3,1,1,2,1,1,2,2,6,4,2,4,6,8,6,5,8,4,6,2,7,5,11,5,5,7,6,11,4,9,6,7,
%U A371457 9,7,5,4,3,8,9,5,5,8,3,5,3,3,1,1,2,1,1,2
%N A371457 Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a progression of the form p, p-q, p+q, where q >= 0.
%C A371457 This sequence avoids one of the six permutations of a set of three integers in arithmetic progression. For example, the set {1,2,3} can be ordered as tuples (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). In this sequence, we avoid (2,1,3) and other progressions of the form p, p-q, p+q, for all q >= 0.
%H A371457 Neal Gersh Tolunsky, <a href="/A371457/b371457.txt">Table of n, a(n) for n = 1..10000</a>
%H A371457 Neal Gersh Tolunsky, <a href="/A371457/a371457.png">Graph of the first 200000 terms</a>
%F A371457 a(n)=1 iff n in A003278.
%Y A371457 Cf. A229037, A100480, A373010, A309890, A371632, A373052, A373111, A361933.
%K A371457 nonn
%O A371457 1,3
%A A371457 _Neal Gersh Tolunsky_, Jun 01 2024